Connection devices are known comprising a coupling which is designed to be mounted on a first fluid transport circuit element and which define an internal channel having a first end segment in communication with the duct of the circuit element and a second end segment, opposite therefrom, which is arranged to receive an endpiece secured to a second circuit element such as a pipe. The second end segment is provided with means for holding the endpiece thereto in leaktight manner, said means comprising an annular retaining element that is elastically deformable in the radial direction and that, at rest, possesses an inside diameter no greater than the outside diameter of the endpiece, and that it is received in a groove of the second endpiece. On its side adjacent to the opening for inserting the endpiece into the second end segment, the groove has a flank that is frustoconical, and on its opposite side it has a flank that is radial, with the flanks being spaced apart from each other in such a manner that the retaining element is axially movable between a position close to the radial flank in which it can be subjected to radial expansion in order to allow the endpiece to pass through while it is being inserted into the coupling, and a position close to the opening in which the frustoconical flank forms means for shrinking the retaining element onto the endpiece when an extraction force is exerted thereon.
That retention technique provides strength against pulling out that is large even when the pressure of the fluid flowing in the circuit is high. Nevertheless, when the circuit is initially put under pressure, the endpiece moves backwards until the retaining element comes into its position close to the opening. Successive variations in pressure tend to generate back-and-forth movements of the endpiece (pistoning) that encourage leaks or seepage to occur through the coupling. In addition, reversal of the endpiece presents the drawback of forming a zone in which fluid is retained between the terminal face of the endpiece and the internal shoulder of the coupling that forms the abutment against the endpiece being pushed into the coupling.